36×36 {-1, +1} matrices of maximal determinant

For a list of Ted Spence's 180 Hadamard matrices of order 36 related
to regular two-graphs on 36 vertices [Sp4],
see his home page.
The 24 order 36 Hadamard matrices
of Goethals-Seidel type found by Spence and Turyn are listed there as well.
The former set is also available at Jennifer Seberry's
home page along
with 15 additional matrices. A single file containing all these matrices,
with duplicates removed, is available from the home page of
Christos
Koukouvinos. He also provides a separate file containing only skew
Hadamard matrices from the above list.

Jennifer Seberry additionally gives three
Williamson-type
matrices and one good
matrix of order 36. The first and third Williamson matrix from her list
are equivalent to the two matrices available in Sloane's
Library of Hadamard Matrices. The first is
also equivalent to the matrix obtained from Paley's (second) construction.

The 22 inequivalent Latin squares of order 6 (available from Brendan
McKay's web site) give rise to 11
inequivalent Hadamard matrices[GS].
See also [CMW] and
[Ca].
These matrices form a subset of the
180 matrices on Spence's list of matrices related to regular two-graphs.

The list of 235
matrices analyzed in [O2] includes all of
the above, as well as some additional matrices collected from the literature
and other sources. The lower bound on the number of equivalence classes
of Hadamard matrices of order 36 given in [O2] is
3,734,467.

Iliya Bouyukliev, Veerle Fack, and Joost Winne have reported the
complete classification of (35,17,8)-designs with an automorphism
of order 3 fixing 2 points and blocks. These give rise to 7238
inequivalent Hadamard matrices [BFW].